Soft matter geometry & topology

The group studies how the shapes of soft materials emerge from the interplay between geometry, mechanics, and topology. Thin elastic sheets, gels, liquid crystals, and other deformable media often store geometric information internally, through gradients of growth, swelling, or molecular alignment, and this information sets the configurations the material can adopt. By treating these problems with the language of differential geometry and the theory of elasticity, the group asks how a prescribed metric or director field translates into curvature, buckling, and the selection of equilibrium shapes.

A central theme is the connection between local geometric frustration and the global morphology of the material. Incompatible reference geometries cannot be realized in flat space, so the material relieves the frustration by wrinkling, folding, forming sharp ridges, or nucleating topological defects. Understanding these mechanisms clarifies natural shape formation in growing tissues and plant organs, and it provides design rules for programmable materials, such as liquid-crystal elastomers and responsive gels, that morph into target shapes on demand.